1

STYLE MIGRATION IN EUROPE

John Paul Broussarda, Jussi Mikkonen

b, Vesa Puttonen

b1

a Rutgers University School of Business,

b Aalto University School of Business

January 28, 2013

1 Corresponding author: Aalto University School of Business, Department of Finance, Runeberginkatu 22-24

FI-00100 Helsinki, Finland. Email: vesa.puttonen@aalto.fi.

2

STYLE MIGRATION IN EUROPE

Abstract

This paper complements the existing literature on style migration by examining value and

size premiums throughout Europe. Information from more than 25 European markets

indicates an average value premium of 9.58% per year. The primary determinants of the

persistent value outperformance are: 1) value firms migrating to a neutral or growth portfolio,

and 2) growth stocks that migrate to neutral or value portfolios. Size factors are not as

prominent, but combining size helps better understand migration. The financial health metric,

F_SCORE, helps discover outperforming stocks ex ante, and provides preliminary evidence

on the probability of migration.

3

1. INTRODUCTION

Within an efficient market context, investors should not be able to consistently outperform

the market using investment strategies based on style or market capitalization. They should

also not be able to consistently find mispriced securities using fundamental analytical

techniques. A plethora of evidence exists, however, detailing anomalous behaviour in

financial markets. Much of the research relates to investment style (value vs. growth) or firm

size (small-cap or large-cap) effects. The consensus indicates that style and size are

characteristics that may help generate above market returns.

The focus of this effort is to evaluate the effects of style and size premia when firms migrate

across various style-size classifications. Two questions are addressed. First, what are the

impacts of migration on stock returns in Europe? Second, how might the incorporation of a

fundamental financial health metric provide a better understanding of the migration issue?

We address the first question by providing an out-of-sample test of Fama and French (2007)

using European data. We address the second question by applying the methodology of

Piotroski (2000), namely the F_SCORE metric, to our data.

A large European database incorporating variables associated with style, size, and financial

health covering the period 1980-2011 indicates the following results. First, migration plays a

major role in driving both value and size effects in European stock markets. The value effect

is found to be 9.58%, on average, and is caused mainly by value stocks migrating to a growth

category. Stocks that do not migrate contribute very little to the value premium. Second, size

effects exist only in the early years of the data. The disappearance of the size effect has been

documented in several markets (see van Dijk (2011) for a summary), although recent

European evidence is scarce. Over the entire period evaluated, the size effect is found to be

an insignificant -0.23%.

Finally, this study documents that the Piotroski (2000) F_SCORE is able to increase the

returns of investment style decisions, but only for small stocks. Preliminary evidence on

migration probability is provided in that small-cap stocks with a very high F_SCORE are

more likely to migrate favourably than stocks with a very low score.

After a review of the literature, a discussion of the data used and portfolio formation specifics

incorporated follows. Results are presented, followed by concluding remarks.

4

2. LITERATURE REVIEW

The origins of differential investment strategy performance can be traced to Graham and

Dodd (1934), who argue that value strategies outperform the market. Basu (1977) found that

stocks with low P/E-ratios outperformed stocks with higher P/Es. Chan et al. (1991) further

notice that in addition to low P/E, outsized returns are also produced by high book to market

ratio and cash flow yield (or conversely low P/BV and P/CF).

One way of explaining the outperformance of value strategies is that the strategies are

fundamentally riskier. The most notable proponents of this explanation are Fama and French

(1992), who argue that investors who follow a value strategy take on more risk. The outsized

returns are simply a compensation for extra risk. The riskiness of value stocks can also be

interpreted as financial distress (Piotroski (2000)). This view is supported by the finding

(Fama and French, (2005)) that low P/BV companies have a consistently lower return on

equity than high P/BV companies. Furthermore, Chen and Zhang (1998), and Fama and

French (1992) find a clear relation between low P/BV, high amounts of debt, and other

financial measures of risk.

Griffin and Lemmon (2002) examine the relationship between the value premium and default

risk and also find that low P/BV firms earn superior returns. The return difference between

low and high P/BV companies that are in financial distress, however, is more than twice as

large as the return in other groups. The authors assert that companies with high distress risk

might be the most likely to be mispriced.

Vassalou and Xing (2004) apply an option pricing model to assess a company’s probability of

default using US data between 1971 and 1999. They find that default risk is strongly related

to a company’s size and P/BV characteristics. High default risk firms earn superior returns,

but only when they have a low market capitalization and low P/BV.

The behavioural school of thought offers an alternative point of view on why the value effect

exists. Lakonishok et al. (1994) argues that the risk-based explanation for the outperformance

of value strategies lacks support. The more plausible explanation for this outperformance is

behavioural. Investors simply make consistent mistakes in estimating stock prospects. As

rosy projections turn out to be too optimistic, glamour, or growth, stocks subsequently

5

underperform. Past winners become losers, and non-glamour, or value, stocks become

winners.

Analyst behaviour might also play a role in the avoidance of value stocks. Stickel (2007)

finds that analysts do not recommend low P/BV companies. Instead, they prefer high P/BV

glamour (growth) firms which have performed strongly in the short term, i.e. momentum

stocks. These stocks also tend to have high forecasted earnings growth. Stickel (2007) argues

that analysts are simply incentivized to recommending these stocks, but also notes that

analysts might confuse stocks that have high earnings growth with stocks that have price

appreciation potential.

Another factor to consider is time horizons. As proposed by De Long et al. (1990), Shleifer

and Vishny (1990), and indicated by Lakonishok et al. (1994), investors’ time horizons

simply may be too short to wait for value strategies to pay off. Institutional money managers

for instance cannot follow a value strategy as it might underperform the benchmark index

over myopic time periods. This short-term underperformance might result in career risk for

institutional investors. Glamour stocks may be easier to justify to clients because they appear

to the prudent choice.

The international evidence on the size effect tends to be consistent with that found in the US.

Van Dijk (2011) finds that small companies tend to outperform large companies in 18 out of

19 countries investigated. According to van Dijk (2011), some explanations for the size effect

are liquidity, investor behaviour and data mining. One of the interesting aspects of the size

effect is its reduced prominence over time. The size effect seems to have “disappeared” in

many markets. Although the empirical evidence supporting a less prominent size effect is

mainly concentrated in the US, the dataset evaluated in this effort also shows a fading size

impact in Europe.

The idea of buying winning value stocks based on accounting fundamentals is not new.

Previous papers such as Lev and Thiagarajan (1993) and Abarbanell and Bushee (1997) find

that certain financial indicators are able to predict future changes in earnings. Piotroski

(2000) takes a step further and combines these signals into a simple measure, the F_SCORE,

to create portfolios. He finds the F_SCORE to be a useful indicator of future portfolio

performance.

6

Fama and French (2006b) utilize fundamental analysis tools, including the Piotroski (2000)

F_SCORE, in an effort to examine the relationship between P/BV, expected profitability and

expected investment to future profitability. Even though they confirm the F_SCORE does

predict future profitability, the authors disagree with the mispricing argument. Fama and

French (2006b) conclude that tests based on valuation cannot reveal how the relation between

average returns and P/BV can separate rational risk and irrational beliefs.

Fama and French (2007) focus on migration and document the following findings in the US

markets over 1927-2006. First, the value premium is due to value stocks migrating to neutral

or growth portfolios. Second, growth stocks that earn low returns and migrate to neutral or

value portfolios also contribute to the value premium. The final determinant of the value

premium is that value stocks that do not migrate earn higher returns than growth stocks that

do not migrate. Fama and French (2007) also find that the size premium is almost completely

driven by small stocks migrating to a large-cap portfolio.

Although the value effect and the mean reverting nature of valuation factors are well-known,

the role of style migration’s impacts on portfolio returns is not as clear. It is here where

paying more attention to style-size migration characteristics becomes useful.

3. DATA AND PORTFOLIO FORMATION

The first step in the sample selection process screens for publicly listed companies in Europe

during 1980-2011. To be included in the sample, a company is required to have sufficient

data on price-to-book, market capitalization, and stock returns. We require the following

data: 1) Book value of equity is available at the end of December, 2) Market capitalization is

available at the end of June, and 3) Monthly stock returns for the entire year need to be

available.

A further requirement is that a company’s fiscal year must end in December. Accounting

data are collected from Worldscope using Thomson One Banker. The data for market

capitalization and returns are from Datastream. To identify companies acquired by other

companies, data from SDC Platinum are used. The merger and acquisition data include

35,255 observations during 1980-2011. Target companies are matched by their Datastream

codes, Worldscope tickers or SEDOL codes. The number of firm-year observations included

7

in the sample is 52,154. Figure 1 shows the full sample of portfolio returns over the time

horizon evaluated. The aggregate sample tends to follow the MSCI composite rather closely.

Following Fama and French (2007), portfolio returns are measured from the end of June each

year. The annual buy-and-hold returns are calculated as the sum of monthly returns. The

return data (including dividends) is obtained from Datastream. All portfolios are value-

weighted and rebalanced at the end of each June. The benchmark index for the aggregate

sample is MSCI Europe. Excess returns are calculated as a portfolio’s return less the return of

the benchmark index during the respective month.

The scarcity of available data in the 1980s is clearly seen in Figure 2. The selection of 1980

as the starting year was mainly due to the limitations in Thomson ONE Banker — earlier data

simply are not available. Although this does not cause problems in the aggregate sample of

52,154, analysis by country and region are somewhat limited because the analysis requires

creating six portfolios per year. As can be seen in Table 1, the number of observations

naturally varies between countries. Expectedly, the United Kingdom, France, and Germany

are the countries with most observations. The price-to-book ratios are mostly gathered at the

total sample median of 1.63, with Eastern European countries having lower valuations. This

is most likely due to the fact that stock exchanges in Eastern Europe have a shorter history

than their Western European counterparts. Variations in the companies’ market

capitalizations can also be seen. Central and Western European companies tend to dominate

the sample by both average and median market capitalization.

Following Fama and French (2007), stocks are sorted into three valuation categories by their

price-to-book ratios. The lowest 30% P/BV forms the value (V) group, the highest 30% the

growth (G) group and the middle 40% are neutral (N) stocks. The second step is to divide

stocks into two size categories, small-caps (S) and large-caps (L) by their market

capitalization. The cut-off point for S and L in year t is the median market capitalization for

the benchmark index at t. This results in six different size-P/BV portfolios:

1. SV — Small-cap Value

2. SN — Small-cap Neutral

3. SG — Small-cap Growth

4. LV — Large-cap Value

5. LN — Large-cap Neutral

6. LG — Large-cap Growth

8

Portfolios are formed at the end of June each year and rebalanced annually. The first portfolio

starts June 1980 and the last June 2010. Thus the last data point for the final portfolio is from

June 2011. The selection of June as the starting year follows Fama and French (2007) to

prevent look-ahead bias. Since companies with negative book value cannot be ranked, they

are excluded from the portfolio formation.

Over time, style classifications can follow two general types of migration: 1) migration

between the six size-P/BV portfolios and 2) migration out of the six portfolios. In the latter

case, a stock will end up in one of the following portfolios:

1. “Good Delist”

2. “Bad Delist”

3. “Neg”

4. “NA”

A stock migrates to the “Good Delist” portfolio if it is acquired during year t. The “Bad

Delist” portfolio consists of stocks that disappear for reasons such as bankruptcy, or not

meeting listing requirements. The “Neg” portfolio consists of companies with negative book

equity and the “NA” includes stocks with missing data for book equity, or the delisting

reason is not known.

The migration portfolios are combined into 24 summarised portfolios. Each size-P/BV

portfolio is split into four broad movement categories:

1. Same: stocks that stay in the same portfolio when portfolios are rebalanced. This

category also includes stocks in the “NA” portfolio.

2. dSize: small-cap stocks that move into large-cap portfolios and vice versa.

3. Plus: stocks that move towards growth portfolios (from value or neutral) or are

acquired by another company (“Good delist”).

4. Minus: stocks that move towards value portfolios or are delisted due to a negative

event (“Bad delist”) or their book value goes negative (“Neg”).

Subsequently, the average annual contributions to the size-P/BV portfolios by each migration

type can be examined. Migration in the size spectrum contributes to the size premium. Also,

migrating stocks with different P/BV characteristics contribute to the value premium.

Contribution comes from two factors, namely the frequency and the magnitude of returns for

9

migrating stocks. The returns of each migration type are calculated relative to the market

return.

Because migrating stocks can be traced at an individual level, this allows several ways to

examine the characteristics that make them migrate. In order to study whether migration can

be predicted, the method outlined in Piotroski (2000), namely the F_SCORE, is applied.

To calculate the F_SCORE, accounting data from the Worldscope database are used. The

number of observations for small value stocks is 13,610 and 2,006 for large value stocks. The

data in this section is smaller than the original dataset due to the increased requirements for

calculating the F_SCORE.

The F-score is defined as the sum of the following binary signals:

The components of the F_SCORE are described below. The variable is equal to one if the

condition is filled, zero otherwise.

1) : the company’s return on assets is positive in year t

2) : ROA in year t is larger than ROA in year t-1

3) : cash flow from operations is positive in year t

4) : cash flow from operations in year t is higher than net income before

extraordinary items in year t (scaled by beginning-of –the-year total assets)

5) : gross margin ratio in year t is higher than the gross margin ratio in year t-1

6) : asset turnover ratio in year t is higher than the asset turnover ratio in year t-1

7) : leverage ratio (long-term debt to average total assets) in year t is lower than

the leverage ratio in year t-1

8) : current ratio in year t is higher than the current ratio in year t-1

9) : the company did not issue equity during year t

10

The first four variables are associated with profitability. As value firms typically have a poor

historical performance in generating earnings or cash flows (Fama and French 1995;

Piotroski 2000), these four variables are able to separate companies that can generate profits.

ROA and CFO are defined as net income before extraordinary items and cash flow from

operations scaled by total assets at the beginning of the year. Therefore, if a company’s ROA

(CFO) is positive, the indicator variable ( ) is equal to one, zero otherwise. In

addition to current financial performance, the recent trend is also considered. is equal

to one if a firm’s current ROA is higher than in previous year, zero otherwise. Finally,

measures the relationship between earnings and cash flow levels to indicate

possible earnings management by the company. Sloan (1996) shows that positive accrual

adjustments (if profits are greater than cash flows from operations) are a bad signal for future

firm performance. Piotroski (2000) adds that the incentives for earnings management are

greater for value firms to avoid possible covenant violations. The variable is

defined as current year’s net income before extraordinary items less cash flow from

operations, scaled by total assets at the beginning of the year. The variable is equal to one if

CFO is larger than ROA, zero otherwise.

The two next signals, and are designed to measure the operating efficiency

of the company. is defined as current year’s gross margin ratio less the gross

margin ratio in the previous year. This variable indicates a possible improvement in pricing

power (or a reduction in costs). The variable is equal to one if the company was able to

increase its gross margin ratio, zero otherwise. is defined as current year’s asset

turnover ratio (total sales scaled by total assets at the beginning of the year) less the asset

turnover ratio in the previous year. The variable is equal to one if the company has managed

to increase its asset turnover ratio, zero otherwise. The asset turnover ratio is a measure of

how efficiently a firm manages its assets. A firm can increase its asset turnover ratio by

generating more sales with the same amount of assets or employ fewer assets to generate the

same amount of sales.

The last three signals, , , , relate to leverage, liquidity and source of

funds, respectively. measures the changes in the company’s long-term debt levels. If

the company is able to reduce its long-term debt compared to previous year, the variable is

equal to one, zero otherwise. measures the change in the firm’s current ratio (current

assets divided by current liabilities) from the previous year. A company can serve its short

11

term liabilities better when the ratio is high. The variable is equal to one if the current ratio

has increased from the previous year, zero otherwise. The last variable, , indicates

whether a company has issued equity in the year before portfolio formation. The variable is

equal to one if a company did not have the need to issue shares, zero otherwise. According to

Piotroski (2000), financially distressed firms that cannot generate adequate cash flows have a

need for external financing and especially the variables and are able to

single out the companies in distress.

4. RESULTS AND ANALYSIS

Table 2 depicts the average returns for each of the six size-P/BV portfolios and the size and

value premiums. The data indicate the presence of a significant value premium (HML) for

European stocks over the 1980-2011 timeframe. The time-series average for the value

premium is a statistically significant 9.58% average annual premium. Fama and French

(2011) also find a value premium (0.55% per month) in Europe. The higher value premium

found in here can partly be explained by larger dataset employed. Fama and French (2011)

cover fewer countries (16 vs 23) with a shorter time span (1990 to 2011). They also report a

larger value premium for small stocks (0.69%) than large stocks (0.42%).

The average annual returns for the SV, SN, SG, LV, LN and LG portfolios are 20.2%, 13.7%,

7.0%, 17.3%, 13.0% and 11.3%, respectively. The corresponding benchmark index return is

12.4% for the same period. The European style portfolio returns are mostly similar to that

presented in Fama and French (2007). In the dataset employed, however, smaller firms do not

outperform their large capitalization counterparts. The size premium (SMB) is -0.23%

annually, but statistically insignificant for the aggregate European sample. The size premium

is positive from 1980-1988, with average returns of 4.20%, but starts to decline after that

period. From 1989 to 2011 the average annual size premium is -2.04%. Apparently, the size

premium has disappeared from Europe after 1988.

12

The development of size and value premiums in time is shown in Figure 3. Graphical

presentation confirms the non-existence of any pattern in size premium. Value premium is

evident, however. Value portfolio outperforms in most of the years and in particular, in the

peak year 2000, the outperformance is 64%. The magnitude of the value effect during the

whole sample is 9.58% which is larger than the 6.1% indicated by Chen et al. (2008) for the

US from 1945 to 2005. As indicated, the value premium found in the European data

evaluated here is larger than that shown in Fama and French (2006a) for the U.S from 1926 to

2004.

Chen and Zhao (2009) argue that if an alternative definition for the size premium is used, the

premium is as robust as ever. The authors find the total size premium to be 0.24% per month

during 1926-2006, 0.30% during 1926-1980 and 0.11% during 1981-2006 with US data. If

however small growth firms are excluded from the sample, the size premium is 0.31%, 0.31%

and 0.30% for periods 1926-2006, 1926-1980 and 1981-2006, respectively. Therefore, the

disappearance of the size premium may be due to the disappointing performance of small

growth firms.

The small growth value portfolio has the lowest returns and highest volatility of all six

portfolios. The average annual return of the small growth portfolio is 7.01%, while the

volatility of annual returns is 24.3%. Following Chen and Zhao’s (2009) argument, if small

growth stocks are excluded from our sample, the annual size premium for 1980-2011 is

3.10%. The t-statistic is 2.02, which represents a statistical significance of 5% for a two-tailed

test. But the size premium disappears also here in the latter period (1988-2011).

Table 3 presents how the size and value premiums behaved in different European countries.

Since the number of observations is low for especially smaller nations, countries are grouped

into fairly similar regions. Countries with many observations are reported independently.

Fama and French (1998) also provide a country-level breakdown of the value effect in 8

European nations from 1975-1995. They document an annual value premium ranging from -

5.99% in Italy to 8.02% in Sweden. They also find a positive value premium in the United

Kingdom, France and Germany, with annual HML factors of 4.62%, 7.64% and 2.75%,

respectively. The data in the Fama and French (1998) study consisted of 686 firms, on

average.

13

Table 3 shows remarkable differences in the HML and SMB factors that illustrate how

divergent the national stock markets have been in Europe. The value premium has been

positive in each region on average, although not statistically significant in Benelux countries.

Moreover, the size effect has both positive and negative magnitudes during the entire period,

which highlights reduced prominence of the size effect. Benelux is the only region where the

size effect is significant.

Table 4 displays the time-series average of migration frequencies. Stocks allocated to each

size-P/BV portfolios are most likely to stay in the same portfolio when the portfolios are

rebalanced at the end of June. Small-cap stocks are less likely to stay in the same portfolio

(67.8%, 59.8% and 59.9%) than large-cap stocks (75.4%, 80.8% and 84.0% for value, neutral

and growth, respectively). The second largest migration type tends to be within the same size

classification. All stocks are more likely to migrate across style definitions rather than

migrate across the size spectrum. For small-cap neutral stocks, migration to the value

classification is more likely (13.8%) than migration to growth (9.8%). However, for large-cap

neutral stocks the situation is opposite, 9.7% migrate to growth, while 7.4% migrate to value.

Interestingly, migration into large-cap territory is almost equally likely for small value stocks

(13.8% in total) and small growth stocks (13.6% in total) when all three valuation categories

are taken into account. This finding is somewhat different to that shown in Fama and French

(2007), who find that small growth stocks are more likely (11.7%) to migrate into the large-

cap category than small value stocks (8.5%). Migration from large to small on the other hand

is somewhat more likely for large cap value stocks (1.9%) than large growth stocks (1.3%).

Stocks that change size tend to stay in the same valuation category. For instance, small cap

value stocks are most likely to migrate to large cap value portfolio (8.0%) rather than the

neutral (5.4%) or growth portfolio (0.4%). This phenomenon holds for all six categories.

Table 5 illustrates the excess returns of the six size-P/BV portfolios and the excess returns by

migration type. Both small-cap and large-cap value stocks (7.8% and 4.9%) beat their growth

counterparts (-5.4% and -1.1%). Small cap value tends to outperform the benchmark (7.8%

average annual excess return) but small cap value stocks that stay in the same category

underperform the benchmark (-2.6%). The outperformance of small-cap value therefore

derives from the stocks that migrate favourably in type or in the size spectrum. To illustrate,

small-cap value stocks migrating to small-cap neutral and growth outperform by 37.1% and

74.0%, respectively.

14

Stocks tend to outperform by a substantial margin when they improve in type or size.

Deterioration in type or size always leads to negative returns. The only exception to this is the

small-neutral (SN) category which migrates to the large value (LV) portfolio. Negative

returns are possible due to the fact that the cut-off level between large and small caps changes

every year. Sharpe ratios tend to increase (see Table 6) when a stock migrates upwards in

either size or value spectrums. Small-cap value stocks as a whole have a Sharpe ratio of 1.30

on aggregate, but their ratio improves considerably as they migrate favourably.

Table 7 presents results connecting migration frequency to excess returns. Although stocks

tend to stay in the same group year over year, non-migrating stocks’ returns tend to be

negligible. Small-cap value stocks that stay in the same category contribute negatively (-

1.6%) to the total portfolio (8.1%), whereas small growth stocks have positive contributions

(1.3 % out of total -5.3%). Further, LV stocks in the “Same” group contribute only 0.8% to

the total portfolio return of 5.4%. The only positive contribution to the LG portfolio is solely

from the non-migrating group.

Contrary to expectations, non-migrating value stocks tend to generate lower performance

than non-migrating growth stocks (SG and LG). Although small value stocks as a whole

perform best (8.1%), the typical small value stock does not migrate, which leads to an

average underperformance of -2.4% for the SV group compared to the benchmark index. This

indicates the significant role of migration due to the fact that the majority of all stocks tend to

stay in the same category.

Value stocks tend to improve in type (SV: 16.3%, LV: 21.3%) almost in equal proportions to

growth stocks that deteriorate (SG: 24.6%, LG: 14.1%). Large value stocks are more likely to

be upgraded (21.3%) than small value stocks (16.3%), which is a similar frequency as

presented in Fama and French (2007). Deterioration in type is more likely for small growth

stocks (24.6%) than their large-cap counterparts (14.1%).

Small-cap neutral stocks are more likely to deteriorate (14.2%) than be upgraded (10.4%).

Interestingly, the opposite is found for large-cap neutral stocks, with 7.5% migrating towards

lower valuation and 10.3% migrating towards higher valuation. This finding is also similar to

Fama and French (2007). Another finding of interest is the difference in returns for neutral

stocks in the “Minus” group. Small neutral stocks tend to generate worse returns (-33.6%)

than large-cap neutral stocks (-18.2%).

15

The role of “Minus” and “Plus” transitions in regard to the value effect is very significant.

Most of the outperformance of small value stocks comes from those stocks that migrate into a

better category (5.8% out of 8.1% total portfolio). The same holds for large-caps (5.3% from

a total portfolio of 5.4%). Growth stocks, on the other hand, that are in the “Minus” category

generate a significant portion of their category’s average excess returns. Small growth stocks

contribute -9.5% to the total -5.3% SG portfolio. The same trend holds for large cap growth

stocks as well (-2.5% of the total -0.6%). The underperformance of growth stocks comes

mostly from the heavy losses in the “Minus” group for both SG and LG.

As expected, migration across the size boundary contributes extensively to the excess returns

of the small-cap portfolios (4.4%, 3.9% and 3.6% for SV, SN and SG, respectively). The

likelihood of crossing the size boundary is almost equal for small value and growth stocks

(13.7% versus 13.6%). The same does not apply for the large-cap stocks. Migration from

large to small caps occurs at almost a tenth of the frequency. The negative contribution for

large-caps ranges from -0.1% to -0.5%, which are significantly smaller figures compared to

small-caps. The reason for this is straightforward and due to the value-weighting of

portfolios. Simply put, migration from small to large is most likely for firms close to the

market cap boundary, which have the largest weights in the portfolios.

Incorporating fundamental variables from a “financial health” perspective indicates that the

F_SCORE is able to increase the returns of a value strategy, although the benefits are

concentrated mainly on small-cap stocks (See Table 8). The results are in accordance with

previous research (Piotroski 2000), i.e. financial health indicators appear to play a significant

role in predicting future returns.

The findings in Table 8 illustrate where the benefits of the F_SCORE are concentrated. For

instance, the F_SCORE directly separates financially weak firms (Low Score) from strong

firms (High Score) when applied to small value stocks. The return difference between the

highest and lowest F_SCORE groups is 24.1%. The return difference between financially

strong firms, and the total sample of small value stocks is 14.7%. For large-capitalization

stocks the return difference between financially strong and weak large companies (2.8%) is

not statistically significant. This implies that financial health matters for small company

migration, but not necessarily for large companies.

In sum, the results to this point are as follows. First, the returns to a small-cap value portfolio

appear driven by stocks migrating to other categories, i.e. stocks are rewarded with a higher

16

P/BV ratio, or they move in the size spectrum. Second, stocks that perform well can be

separated from other stocks in the small-cap value universe using a fundamental based

indicator. The natural question therefore is whether or not these findings are linked. To

evaluate that question, we focus on small-cap value firms.

Stocks are divided into two groups, those that migrate favourably (“Good Migration”) and the

rest (“Other”). “Good Migration” stocks consists of SV stocks moving upwards in value

spectrum (into SN or SG), or the size spectrum (in any of the three LV, LN and LG groups),

or are acquired by another company. Therefore the “Other” category consists of small-cap

value stocks that do not migrate, or are stocks that are delisted for sub-par reasons such as

bankruptcy.

The bulk of outperformance of small-cap value stocks is driven by stocks that migrate in

either the value or size spectrum. Figure 4 illustrates how the probability of migration

changes depending on the firm’s F_SCORE at the portfolio formation period. Companies

with very weak financial strength (F_SCORE of 0 or 1) tend not to migrate or are more likely

to be delisted. The proportion of these stocks in the “Good Migration” category is 15.2%. The

situation is the opposite with the very strong companies (F_SCORE of 8 or 9). Their

proportion in the “Good Migration” category is 30.1%, indicating that financial strength as

measured by the F_SCORE might play a significant role in whether a stock migrates. The

situation is not as clear in the middle range of the F_SCORE values, where the proportion of

stocks migrating favourably hover around 21%-25%.

Table 9 shows the results of the logistic regression for the probability of favourable

migration. Since the outcome is binomial, i.e. a stock migrates favourably or not, we employ

a logistic regression (logit) for the analysis. The odds ratio is 1.0847, which can be

interpreted that a one-point increase in the F_SCORE increases the stock’s probability to

migrate by 8.47%.

The evidence presented here is not enough to draw direct conclusions about migration. The

results are intriguing especially in relation to Chen and Zhao (2009), however. One of their

main findings is that positive earnings shocks drive favourable migration. Stocks that beat

analyst expectations are upgraded in valuation, which explains roughly a third of migration in

their sample. Jiang and Koller (2007) also find that growth stocks tend to have higher returns

on equity and invested capital. The aforementioned findings are interesting because a

17

significant portion of the F_SCORE’s variables consider a company’s profitability and its

improvements in profit performance.

A probable underlying reason for migration therefore is a simple “turnaround” story — a

company’s stock price increases because it is able to deliver better than expected results due

to improving operational efficiency, and thus profitability (as measured by the F_SCORE).

Investors might shun value stocks and remain pessimistic about the companies’ probability to

become more profitable, but the firms manage to surprise positively. Contrarily, without an

improvement in a company’s financials, the stock is not rewarded with an upgrade in

valuation. According to the data from Europe, companies that have a poor financial

performance measure tend to generate sub-par stock performance.

5. SUMMARY AND CONCLUSIONS

This paper examines the role of migration in value and size dimensions by complementing

the existing literature with a European dataset. The main objective of this paper is to provide

an out-of-sample test of Fama and French (2007). A European sample containing 52,154

firm-year observations from over 23 countries is utilized. The overall results suggest that

migration plays a significant role in generating value and size effects. Taking a step further,

this paper evaluates whether migration can be traced to the company level through the

aggregation of accounting data into a financial health measure, the F_SCORE, within a

migration setting.

The data show a significant value premium in Europe with a magnitude of 9.58% per annum.

Secondly, the size effect is insignificant over the entire sample, but appears to be positive if

the smallest growth stocks are omitted from the sample, as in Chen and Zhao (2009).

The value effect in Europe is mainly caused by: 1) value firms that migrate to a neutral or

growth portfolio, and 2) growth stocks that migrate to neutral or value portfolios. These

findings are consistent with Fama and French (2007) and Chen and Zhao (2009). The main

difference between the findings is that value stocks in the US that do not migrate earn higher

returns than growth stocks that do not migrate. The European data set examined here shows a

18

different result: European growth stocks that do not migrate outperform value stocks that do

not migrate.

Portfolio returns can be enhanced with the F_SCORE, but only for small stocks. Small-cap

stocks with a very high score are more likely to migrate favourably than stocks with a very

low score. Further, a logistic regression model is able to pick up a relationship between the

F_SCORE of a stock and its probability to migrate: an increase of 1 unit in the F_SCORE

value for a stock increases the probability of favourable migration by 8.47%.

The value effect appears strong in Europe. Size factors are not as prominent, but combining

size helps better understand migration. The financial health metric, F_SCORE, helps discover

outperforming stocks ex ante, and provides preliminary evidence on the probability of

migration.

19

REFERENCES

Abarbanell, J., Bushee, B., 1997, Fundamental analysis, future earnings, and stock prices.

Journal of Accounting Research. Vol. 35, Issue 1, 1-24.

Banz, R., 1981, The relationship between returns and market value of common stocks.

Journal of Financial Economics. Vol. 9, Issue 1, 3-18.

Basu, S., 1977, Investment performance of common stocks in relation to their price-earnings

ratios: A test of the efficient market hypothesis. Journal of Finance. Vol. 32, Issue 3, 663-

682.

Chan, K.C., 1988, On the contrarian investment strategy. Journal of Business. Vol. 61, Issue

2, 147-163.

Chen, L., Petkova, R., Zhang, L., 2008, The expected value premium. Journal of Financial

Economics. Vol. 87, Issue 2, 269-280.

Chen, N., Zhang, F., 1998, Risk and return of value stocks. Journal of Business. Vol. 71,

Issue 4, 501-535.

Chen, L., Zhao, X., 2009, Understanding the value and size premia: What can we learn from

stock migrations? Working paper. June 2009.

Fama, E.F., French, K.R., 1992, The cross-section of expected stock returns. Journal of

Finance. Vol. 47, Issue 2, 427-465.

Fama, E.F., French, K.R., 1995, Size and book-to-market factors in earnings and returns.

Journal of Finance. Vol. 50, Issue 1, 131-155.

Fama, E.F., French, K.R., 1998, Value versus growth: The international evidence. Journal of

Finance. Vol. 53, Issue 6, 1975-1999.

Fama, E.F., French, K.R., 2006a, The value premium and the CAPM. Journal of Finance.

Vol. 61, Issue 5, 2163-2185.

Fama, E.F., French, K.R., 2006b, Profitability, investment and average returns. Journal of

Financial Economics. Vol. 82, Issue 3, 491-518.

Fama, E.F., French, K.R., 2007, Migration. Financial Analysts Journal. Vol. 62, Issue 3, 48-

58.

Fama, E.F., French, K.R., 2011, Size, value, and momentum in international stock returns.

Unpublished working paper.

French, K.R., Developed Market Factors and Returns. 6 European Portfolios Formed on Size

and Book-To-Market, [online]. Available at:

20

http://www.mba.tuck.darthmouth.edu/pages/faculty/ken.french/data_library.html [Accessed

August 8, 2012].

Graham, B., Dodd, D., 1934, Security Analysis, First Edition. The McGraw-Hill Companies,

Inc. 1934.

Griffin, J., Lemmon, M., 2002, Book-to-market equity, distress risk, and stock returns.

Journal of Finance. Vol. 57, Issue 5, 2317-2336.

Jiang, B., Koller, T., 2007, The truth about growth and value stocks. McKinsey on Finance,

Winter 2007.

Lakonishok, J., Shleifer A., Vishny, R.W., 1994, Contrarian investment, extrapolation, and

risk. Journal of Finance. Vol. 49, Issue 5, 1541-1578.

Lev, B., Thiagarajan, S., 1993, Fundamental information analysis. Journal of Accounting

Research. Vol. 31, Issue 2, 190-215.

Piotroski, J.D., 2000, Value investing: The use of historical financial statement information to

separate winners from losers. Journal of Accounting Research. Vol. 38, Issue 3, 1-41.

Piotroski, J.D., 2005, Discussion of “Separating winners from losers among low book-to-

market stocks using financial statement analysis”. Review of Accounting Studies. Vol. 10,

Issue 2/3, 171-184.

Shleifer, A., Vishny, R., 1990, Equilibrium short horizons of investors and firms. American

Economic Review. May 1990. Vol. 80, Issue 2, 148-153.

Sloan, R., 1996, Do stock prices fully reflect information in accruals and cash flows about

future earnings? Accounting Review. Vol. 71, Issue 3, 289-315.

Stickel, S.E., 2007, Analyst incentives and the financial characteristics of Wall Street darlings

and dogs. Journal of Investing. Fall 2007. Vol. 16, Issue 3, 23-32.

Van Dijk, M., 2011, Is size dead? A review of the size effect in equity returns. Journal of

Banking & Finance. Vol. 35, Issue 12, 3263-3274.

Vassalou, M., Xing, Y., 2004, Default risk in equity returns. Journal of Finance. Vol. 59,

Issue 2, 831-868.

21

Table 1. Firm-Year Observations Per Country

This table illustrates the market capitalizations and price-to-book ratios by the nation of each

company. The country codes and book equity are obtained from Worldscope. Market

capitalizations for each observation at June t are obtained from Datastream. P/BV is the

market capitalization at June t divided by the book equity at December t-1. Forming

portfolios in the end of June is due to allowing enough time for the publishing of the financial

reports to mitigate look-ahead bias.

Market Cap P/BV

Region / Country n Mean Median Mean Median

North Europe / Scandinavia

Denmark 1572 362 58 2.09 1.13

Finland 825 690 107 3.69 1.71

Norway 1694 683 74 2.42 1.48

Sweden 1554 499 34 3.76 2.22

Central / Western Europe

Austria 1021 548 81 2.35 1.37

Belgium 1033 630 116 2.66 1.38

France 8612 1323 74 3.24 1.62

Germany 6938 1446 60 3.38 1.80

Ireland 763 1072 118 2.52 1.75

Luxembourg 321 1963 238 2.67 1.30

Netherlands 2061 2622 221 3.54 1.71

Switzerland 1311 1289 175 3.82 1.44

United Kingdom 13237 1363 67 4.39 1.80

Central / Western Europe (misc.) 232 617 79 3.57 1.52

Southern Europe

Greece 2523 352 57 2.47 1.43

Italy 2261 1553 168 3.51 1.58

Spain 1898 2958 414 2.61 1.70

Portugal 597 731 86 2.03 1.18

Southern Europe (misc.) 413 654 190 2.82 1.60

Eastern Europe

Bulgaria 303 29 2 2.35 0.76

Czech Republic 212 1209 50 1.08 0.71

Hungary 350 467 50 1.39 1.06

Poland 1598 423 60 2.58 1.47

Slovakia 51 83 4 0.64 0.43

Slovenia 111 204 27 0.99 0.83

Eastern Europe (misc.) 663 78 28 1.54 1.06

TOTAL SAMPLE 52,154 1257 79 3.32 1.63

22

Table 2. Descriptive Statistics of Average Annual Returns

This table presents the average annual returns (%) of all six size-P/BV portfolios and the size (SMB) and value (HML) premiums during 1980-

2011. The last three columns also depict the size effect excluding small growth stocks. Six value-weighted portfolios are formed at the end of

each June t: SV, SN, SG, LV, LN and LG. Small-caps (S) are below the median market capitalization of MSCI Europe and large-caps (L) are

above it at each June t. Stocks are further divided into three groups based on their P/BV: Value (V) stocks are the bottom 30%, Neutral (N)

middle 40% and Growth (G) the top 30%. SMB is defined as the return difference between small-cap (SV, SN and SG) and large-cap stocks

(LV, LN and LG) calculated from monthly return data. SMB excluding small growth stocks is defined as the return difference between small-cap

(SV and SN) and large-cap stocks (LV, LN and LG). HML is defined as the return difference between value stocks (SV and LV) and growth

stocks (SG and LG). P/BV is calculated by dividing market cap at the end of June t by book equity at the end of December t-1. Portfolios are

rebalanced at the end of each June. Mean return differences are tested using the t-Statistic by utilizing the two-tailed t-test. Symbols *, ** and

*** illustrate statistical significance levels of 10%, 5% and 1%, respectively.

SMB Excluding Small Growth (SG) Stocks SMB

SV SN SG LV LN LG HML Full

Sample 1980-88 1988-2011

Full Sample

1980-88

1988-2011

Mean 20.20 % 13.74 % 7.01 % 17.30 % 13.01 % 11.33 % 9.58 % -0.23 % 4.20 % -2.04 % 3.10 % 7.97 % 1.10 % Standard Error 3.52 % 3.19 % 4.36 % 3.26 % 3.07 % 3.28 % 2.65 % 1.44 % 1.85 % 1.76 % 1.53 % 2.17 % 1.83 %

t-Statistic 2.76*** 0.56 -1.69* 1.58 0.26 -0.53 3.62*** -0.16 2.27** -1.16 2.02** 3.67*** 0.60

Median 21.51 % 18.19 % 13.03 % 20.07 % 15.97 % 13.50 % 8.15 % 1.76 % 5.94 % -4.75 % 4.56 % 9.65 % -0.25 % Maximum 63.45 % 39.76 % 40.08 % 52.90 % 42.85 % 46.97 % 64.16 % 13.24 % 11.35 % 13.24 % 19.36 % 15.15 % 19.36 % Minimum -27.33 % -33.56 % -64.79 % -46.59 % -22.99 % -27.48 % -14.87 % -17.72 % -5.27 % -17.72 % -9.64 % -6.16 % -9.64 % Skewness -0.36 -0.74 -1.37 -1.22 -0.32 -0.57 1.84 -0.09 -0.62 0.31 -0.04 -1.33 0.42

Kurtosis 0.19 0.15 2.07 4.05 -0.49 0.08 5.76 -0.91 -0.56 -0.68 -1.30 2.05 -0.97

23

Table 3. Size and Value Premiums by Region: 1980-2011

This table presents the average annual returns (%) of the six size-P/BV portfolios and the size

and value premiums by geographical region. Six value weight portfolios (SV, SN, SG, LV,

LN and LG) are formed at the end of June t of each year. The portfolios are formed at the

intersection of two size groups: small-cap (S) and large-cap (L). The cut-off value for small-

caps and large-caps is the median market capitalization of the MSCI Europe. Companies are

divided into three P/BV groups: value (V, bottom 30%), neutral (N, middle 40%) and growth

(G, top 30%). Market capitalization at the end of June t is used to form the size groups and is

obtained from Datastream. To form the P/BV groups, book equity at December t-1 is

obtained from Worldscope and combined with the market capitalization data at June t. The

HML factor is the return difference between value stocks (SV and LV) and growth stocks

(SG and LG). The SMB factor is the return difference between small stocks (SV, SN and SG)

and large stocks (LV, LN and LG). The Benelux category includes Belgium, Netherlands and

Luxembourg. Central Europe consists of Austria, Czech Republic, Hungary, Poland,

Slovakia, Slovenia and Switzerland. Southern Europe is comprised of companies from

Greece, Spain and Portugal. Scandinavia includes Denmark, Finland, Norway and Sweden.

Tests for statistical significance are performed for the HML and SMB factors by utilizing the

two-tailed t-test. Symbols *, ** and *** illustrate statistical significance levels of 10%, 5%

and 1%, respectively.

Country / Region n SV SN SG LV LN LG HML SMB

United Kingdom 13237 19.4 17.2 10.9 18.7 13.5 13.0 7.1*** 0.8

France 8612 27.8 17.2 12.3 20.7 15.5 10.3 12.9*** 3.6

Germany 6938 16.6 8.6 1.7 17.1 10.5 10.9 10.5*** -3.9*

Italy 2261 18.8 5.1 10.6 5.3 16.6 8.7 4.9* 1.1

Benelux 3415 19.7 16.9 17.2 22.5 15.8 11.9 0.7 7.5***

Central Europe 4654 22.0 15.3 2.5 23.7 12.0 8.6 12.2*** -0.7

Southern Europe 5018 15.5 11.7 1.9 14.8 14.3 9.8 9.3** -2.4

Scandinavia 5645 18.6 14.6 13.0 15.7 13.7 7.1 5.9* 1.1

24

Table 4. Average Transition Frequencies for Stocks Migrating Within or Exiting from

the Six P/BV Portfolios: Years 1980-2011

This table presents the average annual value-weighted transition proportions for migrating

stocks within the six P/BV portfolios and the four leaving portfolios during the 1980-2011

period. Six value weight portfolios (SV, SN, SG, LV, LN and LG) are formed at the end of

June t of each year. The portfolios are formed at the intersection of two size groups: small-

cap (S) and large-cap (L). The cut-off value for small-caps and large-caps is the median

market capitalization of the MSCI Europe. Companies are divided into three P/BV groups:

value (V, bottom 30%), neutral (N, middle 40%) and growth (G, top 30%). “Good Delist”

companies are acquired by another company during the year. “Bad Delist” portfolio consists

of companies delisting due to sub-par reasons such as bankruptcy or not meeting listing

requirements. “Neg” category includes companies with negative book value after a year of

portfolio formation. Stocks that cannot be classified in any of the other categories due to

unavailable data belong into the “NA” portfolio. Market capitalization at the end of June t is

used to form the size groups and is obtained from Datastream. To form the P/BV groups book

equity at December t-1 is obtained from Worldscope and combined with the market

capitalization data at June t. To identify the “Good Delist” companies, data from SDC

Platinum is obtained.

AVERAGE TRANSITION FREQUENCIES

SV SN SG LV LN LG

GOOD

DELIST

BAD

DELIST NEG NA

SV 67.8 14.9 0.9 8.0 5.4 0.4 0.5 0.1 0.6 1.4

SN 13.8 59.8 9.8 0.5 10.2 3.8 0.6 0.2 0.2 1.0

SG 2.1 21.6 59.9 0.0 0.8 12.8 1.0 0.4 0.5 0.9

LV 1.7 0.2 0.0 75.4 20.5 0.3 0.5 0.1 0.1 1.3

LN 0.3 0.5 0.0 7.4 80.8 9.7 0.7 0.0 0.1 0.5

LG 0.2 0.3 0.8 0.3 13.3 84.0 0.2 0.1 0.5 0.4

25

Table 5. Average Annual Excess Returns and t-Statistics for Migrating Stocks

Panel A of this table presents the average annual returns for the migrating stocks above the benchmark index MSCI Europe during 1980-2011.

The total column depicts contains all the stocks of that particular style. The leftmost column reports the starting portfolio whereas the rest of the

columns depict the portfolio where the stock migrates. For instance, small value stocks (SV) that migrate to large-cap value category (LV) return

16.9% more than the benchmark index on average. The average annual return of the benchmark index was 12.4% during the 1980-2011 period.

Panel B represents the corresponding t-statistics for the excess returns (compared to MSCI Europe) of the migration portfolios. Symbols *, **

and *** illustrate statistical significance levels of 10%, 5% and 1%, respectively.

Panel A.

AVERAGE ANNUAL EXCESS RETURNS

TOTAL SV SN SG LV LN LG GOOD DELIST BAD DELIST NEG NA

SV 7.8 -2.6 37.1 74.0 16.9 46.8 164.1 36.2 -46.9 -39.3 17.7

SN 1.3 -33.8 0.1 32.7 -9.6 29.7 60.7 41.3 -57.1 -27.4 -16.9

SG -5.4 -87.9 -32.9 0.8 5.0 4.9 35.1 11.8 -56.7 -37.5 -37.8

LV 4.9 -19.8 38.7 N/A 0.9 26.4 42.1 4.3 -60.0 -24.1 -10.7

LN 0.6 -53.2 -23.4 -12.1 -18.3 -0.1 27.6 20.0 -38.6 -19.4 4.2

LG -1.1 -87.2 -49.1 -19.3 -63.5 -18.2 2.4 7.1 -80.7 -50.2 -3.1

Panel B.

t-Statistics

TOTAL SV SN SG LV LN LG

SV 2.95*** -0.96 11.00*** 5.57*** 4.03*** 7.33*** 5.01***

SN 0.54 -10.34*** 0.04 8.54*** -0.74 4.99*** 9.69***

SG -2.04** -11.32*** -9.74*** 0.29 -2.16** 0.58 8.17***

LV 1.82* -3.16*** 1.57 N/A 0.3 7.60*** 2.12**

LN 0.27 -9.44*** -5.32*** -1.01 -4.80*** -0.05 8.59***

LG -0.53 -4.49*** -8.39*** -2.54** -3.34*** -6.01*** 1.11

26

Table 6. Median Sharpe Ratios for the Six Size-P/BV Portfolios

This table presents the median annual Sharpe ratios for the portfolios during 1980-2011. The

risk-free rate is the average 6 month LIBOR rate for the corresponding period and is obtained

from Datastream. The leftmost column reports the starting portfolio whereas the rest of the

columns depict the portfolio where the stock migrates during the year.

MEDIAN SHARPE RATIOS

TOTAL SV SN SG LV LN LG

SV 1.30 0.90 2.74 1.56 1.61 1.62 3.09

SN 0.93 -1.82 0.69 2.03 -0.15 1.59 2.65

SG 0.53 -1.99 -1.21 0.63 -2.03 0.24 1.71

LV 0.93 -0.61 0.69 N/A 0.34 1.75 0.59

LN 0.58 -1.79 -0.81 -0.08 -0.69 0.40 1.79

LG 0.45 -1.47 -1.80 -0.96 -1.02 -0.55 0.47

27

Table 7. Average Annual Excess Returns, Average Transition Vectors and Average Contributions to Average Excess Returns:

Period 1980-2011

This table presents the average excess returns, average transition vectors and average contributions to the excess return for each size-

P/BV portfolios. Average excess return is defined as the average of the annual value-weight returns in excess of the market return for

the year after portfolio formation for all stocks in a size-P/BV portfolio (Total), or for the Minus, Same, Plus or dSize groups of the

portfolio. The Minus group consists of stocks that are downgraded in valuation or delisted due to sub-par reasons. The Same group

includes stocks that do not migrate or data is not available for the next year. Stocks that are upgraded in valuation or acquired by

another company are included in the Plus portfolio. Small (large) stocks that move into large-cap (small-cap) category are included in

the dSize group. The year t transition vector for a portfolio is the fraction of the aggregate market cap of the portfolio when formed at

the end of June of year t that is in the Minus, Same, Plus or dSize group at the end of June t+1. The average transition vector is the

average of the annual vectors. The Minus, Same, Plus or dSize group’s contribution to a portfolio’s average return for year t is the

fraction of the year t market cap that migrates to the group in t+1 times the value-weight average excess return for the group from t to

t+1. The average contribution to excess return is the average of the annual contributions. The average annual value-weight market

return is 12.4% for June 1980 to June 2011.

AVERAGE TRANSITION VECTOR AVERAGE EXCESS RETURN

AVERAGE CONTRIBUTION TO

EXCESS RETURN

TOTAL MINUS SAME PLUS dSIZE MINUS SAME PLUS dSIZE MINUS SAME PLUS dSIZE

SV 8.1 0.7 69.2 16.3 13.7 -51.7 -2.4 36.8 34.3 -0.5 -1.6 5.8 4.4

SN 1.8 14.2 60.8 10.4 14.5 -33.6 -0.7 28.8 37.1 -5.0 -0.4 3.3 3.9

SG -5.3 24.6 60.8 1.0 13.6 -35.5 0.6 3.8 31.8 -9.5 1.3 -0.7 3.6

LV 5.4 0.2 76.7 21.3 1.8 -31.7 1.1 25.8 -14.4 -0.3 0.8 5.3 -0.5

LN 1.0 7.5 81.3 10.3 0.8 -18.2 0.0 27.1 -36.8 -1.3 0.1 2.4 -0.2

LG -0.6 14.1 84.4 0.2 1.3 -19.1 2.4 13.3 -37.3 -2.5 2.0 0.0 -0.1

28

Table 8. Descriptive Statistics for Small-Cap and Large-Cap Value Stocks Based on Fundamental Signals

This table presents the average annual returns, number of observations, Sharpe ratios and tests of statistical significance for small

value stocks and large value stocks. Low Score portfolio consists of stocks with a F_SCORE of 0 or 1 and High Score portfolio of

stocks with a F_SCORE of 8 or 9. All portfolios are value-weighted. The Sharpe column indicates the median annual Sharpe ratios for

the portfolios from 1981-2011. Mean return differences are tested with the t-statistic. Symbols * and ** denote a statistical

significance of 5% and 1%, respectively, using a two-tailed t-test. The median F_SCORE value for both small and large value stocks

is 5.

Small Value Return n Sharpe Large Value Return n Sharpe

All Firms 20.2 % 13610 1.32 All Firms 17.3 % 2006 0.98

0 7.9 % 672 0.64 0 44.6 % 13 0.36

1 9.1 % 695 0.06 1 14.4 % 38 0.56

2 7.4 % 1018 0.06 2 7.9 % 129 0.05

3 14.4 % 1745 0.71 3 16.6 % 330 0.59

4 15.7 % 2227 0.84 4 15.5 % 438 0.49

5 18.9 % 2492 0.69 5 18.9 % 460 0.58

6 25.2 % 2248 1.40 6 20.8 % 325 0.60

7 29.2 % 1530 1.80 7 25.8 % 176 0.98

8 34.6 % 784 1.29 8 23.6 % 76 0.96

9 30.8 % 199 1.26 9 32.0 % 21 0.88

Low Score 10.8 % 1367 0.02 Low Score 20.6 % 51 0.51

High Score 34.9 % 983 1.40 High Score 23.3 % 97 0.54

High - Low 24.1 %

High - Low 2.8 %

t-Statistic 4.04**

t-Statistic 0.29

High - All 14.7 %

High - All 6.00 %

t-Statistic 4.11**

t-Statistic 1.79*

29

Table 9. Logistic Regression Results for Migrating and Non-Migrating Small-Cap Value

Stocks

This table presents the results of the logistic regression applied to the probability of migration for

small-cap value (SV) stocks. Y represents whether a stock belongs to the “Good Migration”

category in the end of June t+1 and X is the F_SCORE value at the end of June t. A value of Y =

1 indicates that a stock has migrated to the “Good Migration” category and a value of Y = 0

indicates that the stock belongs in the “Other” category. “Good Migration” is defined as the

combination of small-cap neutral (SN), small-cap growth (SG), large-cap value (LV), large-cap

neutral (LN), large-cap growth (LG) or a stock which has been acquired by another company.

The “Other” category includes the remaining destinations a small-cap value (SV) stock can have:

it can belong in the same small-cap value (SV) category, its book value can go negative or the

company can be delisted for sub-par reasons. The sample size is 12,614 firm-year observations

during 1981-2011 and is a subset of the original 52,154 firm-year observations.

Logistic Regression Results

Sample Size 12614

Cases With Y = 0 9801 (77.70%)

Cases With Y = 1 2813 (22.30%)

Overall Model Fit

Null model -2 Log Likelihood 13388.16

Full model -2 Log Likelihood 13326.353

Chi-Square 61.807

Degrees of Freedom 1

Significance Level P < 0.0001

Coefficients and Standard Errors

Variable Coefficient Std. Error P

X 0.081277 0.010419 <0.0001

Constant -1.6268

Odds Ratios and 95% Confidence

Intervals

Variable Odds ratio 95% CI

X 1.0847 1.0627 - 1.1070

30

Figure 1. Development of the Reference Portfolio and the MSCI Europe Benchmark

This figure represents the cumulative wealth of an investment in the reference portfolio (Sample)

and the MSCI Europe index (MSCI). The reference portfolio is calculated by forming a single

value-weighted portfolio from the aggregate sample of 52,154 observations. The portfolio is

balanced annually at every June starting from 1980. During the time period 1980-2011 the

reference portfolio returns 12.57% annually on average whereas the MSCI Europe delivers a

12.44% return.

0

500

1000

1500

2000

2500

3000

3500

4000

6/1980 6/1985 6/1990 6/1995 6/2000 6/2005 6/2010

SAMPLE MSCI

31

Figure 2. Firm-Year Observations by Calendar Year

This figure reports the annual number of firm-year observations that form the six value weight

size-P/BV portfolios across the period 1980-2011. Companies are included in the sample if

adequate data for price-to-book, market capitalization and stock returns is available in the

Thomson Financial and Datastream databases. The total amount of firm-year observations in the

sample is 52,154.

0

500

1000

1500

2000

2500

3000

3500

4000

1980 1985 1990 1995 2000 2005 2010

N

Year

32

Figure 3. Annual Size and Value Premiums in 1980-2011

HML is defined as the difference between the average monthly returns of value stocks less the

average monthly returns of growth stocks. Value stocks are the SV and LV and growth stocks

are the SG and LG portfolios. SMB is defined as the difference between the average monthly

returns of small-cap stocks and large-cap stocks during the total sample period of 1980-2011.

-20,00%

-15,00%

-10,00%

-5,00%

0,00%

5,00%

10,00%

15,00%

19

80

19

81

19

82

19

83

19

84

19

85

19

86

19

87

19

88

19

89

19

90

19

91

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

10

Annual Size Premium (SMB)

-20,00%

-10,00%

0,00%

10,00%

20,00%

30,00%

40,00%

50,00%

60,00%

70,00%

19

80

19

81

19

82

19

83

19

84

19

85

19

86

19

87

19

88

19

89

19

90

19

91

19

92

19

93

19

94

19

95

19

96

19

97

19

98

19

99

20

00

20

01

20

02

20

03

20

04

20

05

20

06

20

07

20

08

20

09

20

10

Annual Value Premium (HML)

33

Figure 4. Statistics of Migrating and Non-Migrating Small-Cap Value Stocks

Panel A of this figure represents the proportions of small-cap value stocks that belong in the

“Good Migration” category by their F_SCORE. The “Good Migration” category consists of

stocks that move from small-cap value (SV) category to either small-cap neutral (SN), small-cap

growth (SG), large-cap value (LV), large-cap neutral (LN), large-cap growth (LG) or stocks that

are acquired by another company during the year. The rest of the stocks (“Other”) are stocks that

stay put in the SV category or are either delisted due to sub-par reasons or have negative book

equity the next year. Panel B represents the corresponding number of observations. The final

column in panel B (%) indicates the proportion of stocks belonging in the “Good Migration”

category of all stocks in the corresponding F_SCORE category.

Panel A.

Panel B.

Number of Observations

F_SCORE "Good Migration" "Other" Total %

0-1 175 980 1155 15.2 % 2-3 577 2013 2590 22.3 % 4-5 939 3492 4431 21.2 % 6-7 854 2695 3549 24.1 % 8-9 268 621 889 30.1 %

TOTAL 2813 9801 12614 22.3 %

15,2 %

22,3 % 21,2 %

24,1 %

30,1 %

0,0 %

5,0 %

10,0 %

15,0 %

20,0 %

25,0 %

30,0 %

35,0 %

0-1 2-3 4-5 6-7 8-9